Final Exam- Hypotheses Testing & T-Test Flashcards
Statistics
A branch of mathematics that involves the collection, analysis, and interpretation of data
Descriptive Statistics
Procedures used to summarize a set of data
Inferential Statistics
Are used to analyze data after you have conducted an experiment to determine whether your independent variable had a significant effect
What is Significant?
An inferential statistical test can tell us whether the results of an experiment can occur frequency or rarely by chance.
- Inferential statistics with small values occur frequently by chance.
- Inferential statistics with large values occur rarely by chance.
Null Hypothesis
A hypothesis that says that all difference between groups are due to chance. (i.e., not the operation of the IV)
- If a result occurs often by chance, we say that it is not significant and conclude that our IV did not affect the DV.
- If the result of our inferential statistical test occurs rarely by chance (i.e., it is significant), then we conclude that some factor other than chance is operative.
Directional hypothesis
Specifies exactly how (i.e., the direction) the results will turn out.
Nondirectional hypothesis
Does not specify exactly how the results will turn out.
One-tail t test
Evaluates the probability of only one type of outcome (based on directional hypothesis)
Two-tail t test
Evaluates the probability of both possible outcomes (based on nondirectional hypothesis)
Basic Experiments
- Define IV and DV
- Set Null and Alternative Experimental Hypotheses
- Take a random sample from population
- The sample will represent your population (they have a characteristic in common) - The administration of the IV causes the samples to differ significantly
- The experimenter generalizes the results of the experiment to the general population
Overview of Six Steps of Experiment
- Null Hypothesis
- Alternative Hypothesis
- Level of significance
- Data collection and analysis
- Criterion for evaluating data
- Decision about rejecting/retaining null hypothesis
Null Hypothesis (H0)
- The assumption that there is no difference between groups
- The hypothesis you are trying to disprove in your study
- More generally, that phenomena in your theory are not operating as you predict
Alternative Hypothesis (Ha or H1)
Deals with a specific value or specific difference
- Typically this means testing to see if there are statistically significant differences between groups
- Can be set up as directional or non-directional
- Directional (one-tailed test): Males are expected to be smarter than females on math subsection
- Non-directional (two-tailed test): Males and females will differ, but direction is not known
- -Direction typically guided by theory
- -Direction must be determined prior to data testing/analysis
P-Value
A numerical measure of the statistical significance of a hypothesis test
- Tell us how likely it is that we could have gotten our sample data even if the null hypothesis is true
- Probability
- 0.05 or 0.01
Type I Error
Rejecting the null when the null is actually true
- Evidence suggests that females are smarter than males (but this is correct)
- Accepting the experimental hypothesis when the null hypothesis is true.
- The experimenter directly controls the probability of making a Type I error by setting the significance level (i.e. p-value)
- The p-value is a measure of how likely you are to get this data if no real difference existed (i.e. if the null is true)
- You are less likely to make a Type-I error with a significance level of 0.01 than with a significance level of 0.05
- -However, the more extreme or critical you make the significance level to avoid a Type I error, the more likely you are to make a Type II (beta) error.
Type II (beta) Error
Not rejecting the null when the null is actually false
- Evidence suggests that females and males are equally intelligent (but females are in fact smarter)
- A Type II error involves accepting the null hypothesis and rejecting a true experimental hypothesis
- -Type II errors are not under the direct control of the experimenter
- -We can indirectly cut down on Type II errors by implementing techniques that will cause our groups to differ as much as possible
- -For example, the use of a strong IV and larger groups of participants.
Four potential outcomes
- The null hypothesis is actually true and the test correctly fails to reject the null (there are no difference)
- The null hypothesis is actually false, and the hypothesis test confirms the null is false (there are difference)
- The null hypothesis is actually true, but the hypothesis test incorrectly rejects it (Type I error)
- The null hypothesis is actually false, but the hypothesis test incorrectly fails to reject the null (Type II error)
Lower alpha
Lower chance of Type I error
-Ex: 0.05 alpha means that the chances of rejecting a true null hypothesis equals 5 out of 100
Calculated Value (Test statistic)
Summary of data leads to single numerical value (e.g., Pearson’s correlation r)
P value
Indicates how likely it would be, assuming the null is true, to end up with a sample correlation as large or larger than the computed r.
Critical Value
Value needed to be significant
- Set prior to data analyses
- Determined by alpha level (will be greater if alpha level is lower)
- Sample data statistics will be compared against the critical value
- Allows research to decide whether or not to reject the null
Level of significance
Selecting a preset point on which the p-value must fall
- Standard in psychology is at the 0.05 level
- If p value is smaller than the criterion, the sample is viewed as inconsistent with null
Failing to reject the null (or accepting the null)
Accepting the assumption that the null is true
- Intelligence scores for males and females were not significantly different
- Or…“No significant main effects were found”
Rejecting the Null
Saying that the null is false
- Something is occurring
- Typically indicated by statistically significant differences (e.g. p<0.05)
- Ex: Females scored significantly higher than males
Nonrandom Assignment to Groups
- Random assignment tends to create equal groups in the long run
- As groups get larger, we can place more confidence in random assignment achieving what we want it to
- If we are faced with a situation in which we have fewer potential research participants and we are worried that random assignment may not create equal groups, what can we do?
Correlated assignment
- A method of assigning research participants to groups so that there is a relationship between small numbers of participant
- These small groups are than randomly assigned to treatment conditions (matched assignment)
Matched pairs
- Research participants in a two-group design who are measured and equated on some variable before the experiment
- Typically we measure a variable that could result in confounding if not controlled
- After we have measured this variable, we create pairs of participants that are equal on this variable
- After we have created our matched pairs, we then randomly assign participants from these pairs to the different treatment conditions
Repeated measures
- The same participants are tested in both treatment conditions of our experiment
- The matched pairs are perfectly equal because they consist of the same people or animals tested across the entire experiment
- No extraneous variables should be able to confound this situation because any difference between the participants’ performance in the two treatment conditions is due to the IV.
- In this type of experiment, participants serve as their own controls.
Natural pairs
- Pairs of participants are created from naturally occurring pairs (e.g. biologically or socially related)
Within-subjects comparison
- Refers to a contrast between groups of participants who were assigned to groups through matched pairs, natural pairs, or repeated measures
- We are essentially comparing scores within the same participants (subjects)
- Although this direct comparison is literally true only for repeated-measures designs, participants in matched or natural pairs are the same with regard to the matching variable
Choosing a two-group design
- Random assignment should equate your groups adequately (assuming that you have large groups)
- If you are using 20 or more participants per group, you can feel fairly safe that randomization will create equal groups.
- If you are using 5 or fewer participants in a group, randomization may not work.
Advantages of correlated groups designs
- Control issues
- The three methods for creating correlated-groups designs give us greater certainty of group equality. - Statistical issues
- Correlated-groups designs can help reduce error variation
Error variability
Variability in DV scores that is due to factors other than the IV_ individual differences, measurement error, and extraneous variation (within-groups variability)
*Statistic = Between-group variability/Error variability
Advantages of independent-groups designs
- Similarity
2. Use of correlated-groups designs is impossible in some situations
True experiment
An experiment in which the experimenter directly manipulates the IV.
Ex post facto research
A research approach in which the experimenter cannot directly manipulate the IV but can only classify, categorize, or measure the IV because it is predetermined in the participants (e.g. IV=sex)
t Test
An inferential statistical test used to evaluate the difference between the means of two groups
Degrees of freedom
The ability of a number in a specified set to assume any value
Interpretation of t value
- Determine the degrees of freedom (df) involved
- Use the degrees of freedom to enter a t table
- This table contains t values that occur by chance
- Compare your t value to these chance values
- To be significant, the calculated t must be equal to or larger than the one in the table.
